Lubik-Matthes Natural Rate of Interest

Federal Reserve Bank of Richmond

Lubik-Matthes Natural Rate of Interest

The natural rate of interest is a hypothetical interest rate that is consistent with economic and price stability. There are various estimates of the natural rate in the economics literature, each making certain assumptions about economic interactions. Economists Thomas Lubik at the Richmond Fed and Christian Matthes at Indiana University have devised one such estimate: the Lubik-Matthes Natural Rate of Interest. It is computed using a more flexible economic framework than other popular methods. Their estimate will be updated quarterly.

Latest Reading

Last updated on September 23, 2026

The median estimate for the Lubik-Matthes Natural Rate of Interest was 1.85 percent as of the second quarter of 2026.

        dates,lower16,median,upper84
1967-03-31,0.744604369275948,1.45689988031149,2.11650776613224
1967-06-30,0.671668085688164,1.39303259881128,2.04939718709093
1967-09-30,0.600784381068104,1.43439695577755,2.19080355774573
1967-12-31,0.531692050187073,1.44154874842763,2.28076689888608
1968-03-31,0.477632525064605,1.48858144838905,2.43560273595868
1968-06-30,0.462809586661466,1.51450992664922,2.52331906554508
1968-09-30,0.485802619555007,1.43295172138488,2.3147222073781
1968-12-31,0.479481946641098,1.42560475130663,2.31228388844027
1969-03-31,0.54683735540855,1.51424545348141,2.45048609667985
1969-06-30,0.502502834057527,1.60342362610876,2.72227550734993
1969-09-30,0.532939862455983,1.58975915848696,2.65656973217857
1969-12-31,0.520967915325311,1.52661260984152,2.51379190014845
1970-03-31,0.546726800898474,1.50985084565227,2.43973371490307
1970-06-30,0.522993477585217,1.46272981591804,2.35385714727007
1970-09-30,0.501266126328572,1.41492425488952,2.26780800233761
1970-12-31,0.284412911963784,1.30499941058833,2.21542955127996
1971-03-31,0.331506186512524,1.29944418574839,2.15909220618167
1971-06-30,0.404180158127816,1.38006240792084,2.28064664821749
1971-09-30,0.528323680915064,1.44559786564538,2.30281333729321
1971-12-31,0.658863718600246,1.38110364836499,2.04195337085774
1972-03-31,0.548740003883698,1.35511153606809,2.08514621935289
1972-06-30,0.641675273599271,1.49762146883914,2.29171452427012
1972-09-30,0.631714850683094,1.4787562978568,2.26075174562528
1972-12-31,0.677253713223605,1.5065367819022,2.29048544203902
1973-03-31,0.620319471449663,1.57696689983344,2.49569297874149
1973-06-30,0.209907013621199,1.5145183176087,2.75447408523292
1973-09-30,0.00720221462990361,1.54405554174015,3.05997783337378
1973-12-31,0.113499891796547,1.42499261882337,2.65107056908821
1974-03-31,-0.118254688420472,1.27948408863974,2.54032418554272
1974-06-30,-0.800718740643322,1.24379471420891,3.20349864912574
1974-09-30,-1.1181934049574,1.13200197679649,3.30269644350409
1974-12-31,-0.699420265207757,1.0198758732423,2.57389566784846
1975-03-31,-0.435553693211881,1.03189072857912,2.1679221443637
1975-06-30,-0.0590039002528901,1.14176955624357,2.15133380565422
1975-09-30,0.0971278590713379,1.28028833043135,2.39437297977031
1975-12-31,0.0410772672122182,1.25049801107089,2.37223414430223
1976-03-31,0.105245246796453,1.27836871506426,2.37416951464785
1976-06-30,0.287178250246154,1.34262026709846,2.32331326674689
1976-09-30,0.124348048665974,1.2775016514129,2.3358883828605
1976-12-31,0.063567160752237,1.24070517451541,2.31055620359306
1977-03-31,0.0123678436639833,1.24349351302015,2.3913929183251
1977-06-30,0.136550332652874,1.32211281366277,2.4727577416266
1977-09-30,0.129421529502744,1.33466711308131,2.50957333310861
1977-12-31,0.26196389056943,1.3835809271542,2.47923485039143
1978-03-31,0.271776806941797,1.39072265432731,2.4735901918996
1978-06-30,0.272909298333133,1.50916600111541,2.79221717858241
1978-09-30,0.287686868213325,1.51668669480811,2.78685294987592
1978-12-31,0.338033112425471,1.63427559518898,3.05011142486773
1979-03-31,0.556205453808531,1.61782432949449,2.74106487188501
1979-06-30,0.280839996197655,1.57983750937922,2.94792328001793
1979-09-30,0.434535162275462,1.69701224158659,3.12146279185302
1979-12-31,0.481901079185039,1.90508528359402,3.66782065098862
1980-03-31,0.412733625625872,1.93160786600182,3.82623698252053
1980-06-30,0.331043805660782,1.5561850729297,2.79842201937322
1980-09-30,0.340889282826963,1.51552236368344,2.65933840900452
1980-12-31,0.80460430873296,2.39548189366485,4.70066835887671
1981-03-31,0.934567229821716,2.20699057045789,3.96328009640727
1981-06-30,1.1225363763182,2.31553015654959,4.04412763906962
1981-09-30,1.2110934529308,2.29101410815381,3.86663462806098
1981-12-31,0.930520762199496,1.78761247469246,2.69770416379611
1982-03-31,1.29125311843613,2.21748571626685,3.4834071765274
1982-06-30,1.40868145042027,2.31147201899242,3.61837053849257
1982-09-30,1.05818515836592,1.81385674126639,2.60560225508235
1982-12-31,1.15431456709234,1.88882182907557,2.69464093723512
1983-03-31,1.30352236933302,2.02113162956773,2.86665313155926
1983-06-30,1.45847977342109,2.10603487022696,2.90969532572257
1983-09-30,1.4968939564198,2.28169366026229,3.33069954216292
1983-12-31,1.55060250138531,2.24396277960685,3.17542949730067
1984-03-31,1.58915677855608,2.30275620296881,3.2862583381111
1984-06-30,1.6569722519928,2.46953879958961,3.67209942878053
1984-09-30,1.64085482298545,2.40143028111462,3.52056906883942
1984-12-31,1.4319911981628,2.01948299893995,2.72033360330672
1985-03-31,1.43369465747245,2.0931943594543,2.88414553536721
1985-06-30,1.45220703276695,2.06527548666517,2.78856590709506
1985-09-30,1.54456594990455,2.18421371914315,2.98887227626791
1985-12-31,1.53082948400551,2.13557064568822,2.88685162832137
1986-03-31,1.45129835855335,2.05593938626828,2.76274122862419
1986-06-30,1.40698076887768,1.97003651620216,2.60284951458905
1986-09-30,1.33331831345368,1.88184463254881,2.45507021258443
1986-12-31,1.45024485739677,2.02237505452093,2.68323443574565
1987-03-31,1.40004713264006,1.95629534527869,2.56838185899342
1987-06-30,1.5489347637788,2.17125810070662,2.94631185811273
1987-09-30,1.49476624223584,2.09852196222723,2.81926280736887
1987-12-31,1.50674702620075,2.12084226898653,2.86122615716106
1988-03-31,1.42202979256599,2.00875696060533,2.68147622093469
1988-06-30,1.50438361142767,2.14502358858342,2.92565035295763
1988-09-30,1.58780963825583,2.26153172773282,3.13638692331839
1988-12-31,1.60220600974255,2.26814773692637,3.12657494591529
1989-03-31,1.69129218104225,2.40443620078365,3.38394484822716
1989-06-30,1.63384427535981,2.29176069346077,3.15486633868222
1989-09-30,1.54190607266373,2.14086441561326,2.8765986299229
1989-12-31,1.51582412495068,2.12145770733142,2.85042395811403
1990-03-31,1.54220650049529,2.18677764795032,2.98753133347607
1990-06-30,1.54695064290451,2.20449795090622,3.02866298417571
1990-09-30,1.49128754220643,2.11331367575579,2.86281228050233
1990-12-31,1.33390239743748,1.91281751371746,2.53532421024914
1991-03-31,1.12218115417121,1.70622929534643,2.26687154253837
1991-06-30,1.31805351593175,1.87983461622602,2.4609711568339
1991-09-30,1.3682707716473,1.94337490064744,2.55440768202847
1991-12-31,1.18753398454183,1.7575748119505,2.31860690832784
1992-03-31,1.12218430742174,1.69626799569005,2.24783980276941
1992-06-30,1.2016734061164,1.76621018093427,2.31869465424952
1992-09-30,1.04852723065205,1.6245419115179,2.17098737520829
1992-12-31,1.14832353951119,1.72264195024485,2.27906427891999
1993-03-31,1.12053956393259,1.70185307035697,2.26298339840274
1993-06-30,1.13619502211691,1.72368644115624,2.29388132677031
1993-09-30,1.13241071177128,1.7058114234168,2.26788032128587
1993-12-31,1.11853173550412,1.69197017255966,2.25062243171603
1994-03-31,1.23725244715294,1.80475944374259,2.38140499754582
1994-06-30,1.49939679785123,2.10027449044544,2.76641457674764
1994-09-30,1.51760133271794,2.13378867816734,2.83158969696201
1994-12-31,1.59103179631572,2.24448808117957,3.00732466678173
1995-03-31,1.59538240551044,2.27254306515183,3.0744088025342
1995-06-30,1.53564603429463,2.20452618242645,2.97117435297104
1995-09-30,1.5132143891463,2.18432439845143,2.94252694136842
1995-12-31,1.50633689878321,2.18382038666273,2.94541454998649
1996-03-31,1.38319448043756,2.04168031476892,2.75338265071704
1996-06-30,1.51555422775182,2.20040089090144,2.97736739356422
1996-09-30,1.54356988737983,2.24894848976596,3.05878319098692
1996-12-31,1.52703460040299,2.2291803023976,3.03147844484328
1997-03-31,1.47261457635059,2.17920392375786,2.97773080915305
1997-06-30,1.61346592063916,2.36261913730557,3.24193538556814
1997-09-30,1.5042047169097,2.25321465253174,3.11335113283813
1997-12-31,1.45256651165291,2.19822158527635,3.04355374446914
1998-03-31,1.52662868013613,2.30405455805339,3.21693122211686
1998-06-30,1.48765902785141,2.25922633889859,3.15363155009373
1998-09-30,1.59053526638476,2.39599986087352,3.36446661943164
1998-12-31,1.31102477330621,2.02855489006097,2.81192151838271
1999-03-31,1.35387521053518,2.08019232520615,2.88791348117377
1999-06-30,1.38339585123747,2.10572848453431,2.9221841248114
1999-09-30,1.54394885521123,2.31312157882803,3.23393755304718
1999-12-31,1.60540155496323,2.38947244462272,3.33985147462196
2000-03-31,1.57767581052868,2.35342861573078,3.30160877040861
2000-06-30,1.69135225674821,2.54481973160819,3.61810704502065
2000-09-30,1.56118895927726,2.3615686211807,3.34466257143864
2000-12-31,1.51380750750952,2.29749879410615,3.24361644226903
2001-03-31,1.21246797853444,1.90102810367751,2.6445456490641
2001-06-30,0.955498159022282,1.60779391573086,2.24934979217032
2001-09-30,0.688581318920305,1.35443448203742,1.97737209614386
2001-12-31,0.40647361759128,1.11803483649524,1.74393106860465
2002-03-31,0.714322320864942,1.35890332261401,1.96541074078327
2002-06-30,0.95393509603901,1.58576137334832,2.21392699141647
2002-09-30,0.835386268028907,1.48083774730144,2.09970363786528
2002-12-31,0.502236817780486,1.18713203311854,1.80690588496572
2003-03-31,0.591896064675023,1.2555779814048,1.8724616173659
2003-06-30,0.660606336182725,1.31185267836849,1.92514406981074
2003-09-30,0.786265662270579,1.41962181678913,2.03936793275595
2003-12-31,0.818928661458359,1.44987068028346,2.07293187307623
2004-03-31,0.681025648730338,1.33763536318497,1.97139879942217
2004-06-30,0.638079009604377,1.31120077308448,1.94945020859875
2004-09-30,0.82690689414324,1.45804356321575,2.09519249409762
2004-12-31,1.0071054473436,1.64090110453356,2.30907698578892
2005-03-31,1.13479694956043,1.80534874144001,2.53534332443446
2005-06-30,1.13342865199616,1.80125986195895,2.52541249527131
2005-09-30,1.21046423390849,1.90335877885144,2.65964391652757
2005-12-31,1.24594828309838,1.96333840614523,2.76101092037979
2006-03-31,1.4291690444595,2.20181577181359,3.10100452836609
2006-06-30,1.46513033679643,2.28768325413936,3.26810012531536
2006-09-30,1.3536546975923,2.15097164930047,3.07160999477773
2006-12-31,1.23657244226393,1.99588710740156,2.84296516754475
2007-03-31,1.32784653879157,2.12642787295781,3.03880651879184
2007-06-30,1.28907040762375,2.08541072591136,2.98637955293415
2007-09-30,1.30332288250579,2.11515011032979,3.03646636560358
2007-12-31,1.08585647991276,1.84727388880794,2.66535561345325
2008-03-31,0.303333939567505,1.07850597884725,1.77269961690838
2008-06-30,0.295396834078789,1.05478498485988,1.73703325592875
2008-09-30,0.344385894039378,1.10945752554115,1.81229607113436
2008-12-31,-1.2035961307438,-0.00535279164210523,0.902774798168185
2009-03-31,-0.446894882965351,0.527463565276327,1.31962390790737
2009-06-30,0.155051982172162,0.953769975011906,1.67147982989462
2009-09-30,0.317456602506716,1.07200905667793,1.7703565732184
2009-12-31,0.54556521729163,1.29329617333969,2.02532341261553
2010-03-31,0.0392933796344082,0.84552682030474,1.56426831705558
2010-06-30,-0.0391113451729442,0.780207463252878,1.50409006530591
2010-09-30,0.0625877216466325,0.853601220348229,1.57094459069669
2010-12-31,0.0642147609209821,0.863389824305666,1.58708583198303
2011-03-31,0.189716521287982,0.983522519931383,1.71559497566703
2011-06-30,0.174838892586987,0.996997793583886,1.7480754930617
2011-09-30,-0.0196223318649614,0.824253493948969,1.58101193574611
2011-12-31,-0.0401693496888593,0.779356765091122,1.52536443313877
2012-03-31,0.0343146022560508,0.894311917422723,1.66827486205812
2012-06-30,0.00455831001015927,0.84600948247249,1.60415186383789
2012-09-30,-0.0491768063467228,0.775298946311174,1.52227800973639
2012-12-31,-0.0416701269808462,0.795921311232589,1.54548190418189
2013-03-31,0.0787294058981708,0.871345532218748,1.60189406428067
2013-06-30,0.139755010982005,0.909544694307217,1.62620621128774
2013-09-30,0.159143775299214,0.927554696348064,1.643064971241
2013-12-31,0.147877404817286,0.923017583609988,1.64482775105802
2014-03-31,-0.0162052077456064,0.78366622405864,1.51353429956626
2014-06-30,0.266605838514377,1.015104673639,1.73079196580106
2014-09-30,0.221215154482641,0.970479926974619,1.6788328923155
2014-12-31,0.112741591847698,0.872055044924215,1.58169404853232
2015-03-31,0.169017494991618,0.915207179029468,1.61874759947877
2015-06-30,0.16952750469652,0.938189312826276,1.64853088845936
2015-09-30,0.230649510139914,0.97365456112102,1.68386690644497
2015-12-31,0.137919748937632,0.891961825624139,1.60460575082686
2016-03-31,0.336868704819166,1.06418350629723,1.7696353165161
2016-06-30,0.1950436690151,0.963262472883394,1.68436536120872
2016-09-30,0.387923736324057,1.10692226174061,1.81327979357093
2016-12-31,0.29270130602516,1.00330673604464,1.69582855775694
2017-03-31,0.399799994226096,1.09964980441332,1.79649681670981
2017-06-30,0.554282061762483,1.22559204461957,1.90972342187395
2017-09-30,0.706908558768825,1.35796528686699,2.04494085431114
2017-12-31,0.749915806738967,1.40161907742399,2.0816709211617
2018-03-31,0.849724156330261,1.52149625109149,2.24396206014188
2018-06-30,0.908162689362607,1.57587359627067,2.30678086447218
2018-09-30,0.784059373919493,1.43416725384351,2.10985968894581
2018-12-31,0.81621484611073,1.46855221524267,2.15459691831456
2019-03-31,0.92912285277718,1.58100753145634,2.27857158721248
2019-06-30,1.01857509603854,1.66818468570171,2.37442974726149
2019-09-30,0.958442591212217,1.60017255652718,2.27719875218208
2019-12-31,0.58436899514375,1.24859966990797,1.89161954178807
2020-03-31,0.369939778509268,1.09183721112155,1.76041391864664
2020-06-30,-1.60237439629875,-0.128861578338852,0.950018312054292
2020-09-30,1.28344996123435,1.96914645082883,2.75809591073797
2020-12-31,0.782488000785804,1.48031857051759,2.18375224586046
2021-03-31,0.689094580379003,1.40591979351014,2.10450555779164
2021-06-30,0.724357370793667,1.60107492708541,2.52396866072793
2021-09-30,0.0937509393421357,1.14223605102939,2.04984702824144
2021-12-31,0.344741490881878,1.34998729823085,2.2750930430161
2022-03-31,-0.182197039590723,1.06625681463732,2.09141218094933
2022-06-30,0.202347246206274,1.27369738395525,2.21777961626439
2022-09-30,1.01236846964181,1.87602867685966,2.89980067386833
2022-12-31,1.24754651984533,2.05667461618711,3.0956648260468
2023-03-31,1.3130936059207,2.10342157506267,3.12689395157489
2023-06-30,1.40137633915379,2.15886425689237,3.14209361019924
2023-09-30,1.38743705812881,2.0641241711261,2.88783601183243
2023-12-31,1.3993252992851,2.07158034464838,2.87202489549737
2024-03-31,1.42641910278421,2.15272553230746,3.0732580229372
2024-06-30,1.50023731276751,2.2408492573106,3.20309750146948
2024-09-30,1.44497313022478,2.1498327087019,3.02519322100624
2024-12-31,1.15529054294632,1.79692783302155,2.49260479638505
2025-03-31,1.09245599834572,1.75073957318031,2.46200282987771
2025-06-30,1.34644915659129,2.02176376897133,2.84112437056036
2025-09-30,1.30504982086423,1.97511542007473,2.75971076765038
2025-12-31,1.05079333174762,1.69548092066974,2.37047072669318
2026-03-31,1.08645535116657,1.800417048497,2.5949739548127
2026-06-30,1.14049622084478,1.84979484122078,2.65259095743486

The real natural rate of interest was computed using the procedure described in Thomas A. Lubik and Christian Matthes, "Calculating the Natural Rate of Interest: A Comparison of Two Alternative Approaches," Federal Reserve Bank of Richmond Economic Brief 15-10, October 2015. Further discussion of this approach based on time-varying parameter VARs can be found in Thomas A. Lubik and Christian Matthes, "Time-Varying Parameter Vector Autoregressions: Specification, Estimation, and an Application," Federal Reserve Bank of Richmond Economic Quarterly, vol. 101, no. 4, Fourth Quarter 2015, pp. 323-352.

What Does the Natural Rate of Interest Mean?

The real natural rate of interest is a key concept for understanding and interpreting macroeconomic relationships and the effects of monetary policy. Interest rates equal to the natural rate are consistent with price and economic stability. Rates above the natural rate slow economic activity and price growth, while rates below the natural rate are stimulative. In other words, it is not the level of the natural rate that matters but its value relative to other interest rates.

The natural rate of interest is thought to be determined by economic fundamentals such as productivity shocks or changes in consumer's preferences. The challenge is that the natural rate of interest is a hypothetical construct that cannot be measured directly. Instead, economists have developed various empirical methods that attempt to derive the natural rate from actual data. The Lubik-Matthes estimate is one such approach that applies fewer theoretical restrictions than other popular methods, such as the Laubach-Williams and Holston-Laubach-Williams models produced at the Federal Reserve Bank of New York.

Additional Resources

Methodology behind the Lubik-Matthes Natural Rate of Interest (non-technical version, updated model)

Downloadable data and additional graphs (XLS)

Podcast episode about the Lubik-Matthes Natural Rate of Interest

Suggested Citation

Lubik-Matthes Natural Rate of Interest, Federal Reserve Bank of Richmond, last updated September 23, 2026, https://www.richmondfed.org/research/national_economy/natural_rate_interest.